Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C31 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×C31×C3⋊D15 |
| unambiguous semidirect product | (C3×D5)⋊(D15×C31) |
| unambiguous semidirect product | (C5×D5)⋊(C3⋊D3×C31) |
| Fitting, socle, Hall | C32×C52×C31 ⋊ C22 |
| derived, Hall | C32×C52 ⋊ C22×C31 |
| Hall | C52×C31 ⋊ C2×C3⋊D3 |
| Hall | C32×C31 ⋊ D52 |
| Sylow | C52 ⋊ C2×C3⋊D3×C31 |
| Sylow | C32 ⋊ D52×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D5×C3⋊D15 |
| commutator, cosocle, hypocenter | C32×C52 | C22×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C31 | C22 |
| LCS | G ▷ C32×C52 | |
| UCS | C1 ◁ C31 | |
288 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 704);